Abstract

The paper is concerned with a special class of positive linear operators acting on the space C(K) of all continuous functions defined on a convex compact subset K of R^d, having non-empty interior. Actually, this class consists of all positive linear operators T on C(K) which leave invariant the polynomials of degree at most $1$ and which, in addition, map polynomials into polynomials of the same degree. Among other things, we discuss the existence of such operators in the special case where K is strictly convex by also characterizing them within the class of positive projections. In particular we show that such operators exist if and only if the boundary of K is an ellipsoid. Furthermore, a characterization of balls of R^d in terms of a special class of them is furnished. Additional results and illustrative examples are presented as well.

Autore Pugliese

• Altomare Francesco , Cappelletti Montano Mirella

Tutti gli autori

• ALTOMARE F.;CAPPELLETTI MONTANO M.

Titolo volume/Rivista

Non Disponibile

Anno di pubblicazione

2014

ISSN

0022-247X

ISBN

Non Disponibile

Numero di citazioni Wos

6

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

4

Ultimo Aggiornamento Citazioni

Non Disponibile

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile